Is it possible to have vinyl nearly noise free?

Yes, it is certainly possible. But it’s not for the lazy or the gullible.

Whart and atmasphere discuss the issues and, characteristically, stick to the science. See the US cleaning threads for details on record cleaning. For what it’s worth, I agree about rinsing - pure water, and lots of it.

Agree with Captain_Winters. The   Mobile Fidelity Stevie Ray album on the new Super Vinyl is dead quiet with reduced  (eg absolutely no) groove noise. Up until that purchase, I had believed that other great Mobile Fidelity , Analogue Productions, etc albums were dead quiet. As in all things audio, you can never know what you are missing until you experience  there actually was another step to be taken. 

I was at AXPONA this past weekend. I heard several talks about vinyl cleaning by some experts, The folks from Kirmuss record cleaning systems have done a lot of research into how to best clean a record and backed up their information with detailed microscopic photos of the results. Perfect Vinyl professional record cleaning service also spoke about how they clean records. They get very good results too.Check out their websites for more complete information. In addition I spoke with the folks at Sweet Vinyl Sugar Cube digital pop and click remover. These units are work great and have gotten many endorsements including Mike Fermer. They have a lower priced unit coming out soon, at $1500 it is a little pricey but then lots of gear in this hobby is.As for my system I keep my records clean but I also have an internal pop and click remover in my brain, I just tune out the odd bits of noise, works pretty good.

Whart, If iso propyl alcohol removed the cement from your stylus you need to buy a different cartridge from a different manufacturer. That is just a liability statement from Ortofon of which I have had several and have never damaged one yet. A lot of the stuff stuck to styli will not be removed by simple brushing especially just back to front. If some phono stages accentuate tics and noise then they have a frequency response/correction curve issue.
Just because one copy of a disc is quiet does not mean the whole run will be. They always get noisier towards the end of the run.
Tomic, Last is just freon. Freon is a group of halogenated hydrocarbons used usually as refrigerants and propellants. Freon is a great solvent 

Whoops, hit the green button by accident!

for poler molecules like oils and it evaporates very quickly. If you use the evaporation test you will notice that there is absolutely nothing in last that will not evaporate. 
Theo, the Sugar Cube is like having sex with a rubber on. It may be useful if the record has AIDs but it is not needed at all for a virgin record.